How many design changes has the penny gone through since it was first minted?

Answer 1

US Reverse Designs

Large cents:

• Flowing Hair Chain (1793)
• Flowing Hair Wreath (1793)
• Liberty Cap (1793-1796)
• Draped Bust (1796-1807)
• Classic Head (1808-1814)
• Coronet (1816-1839)
• Braided Hair (1839-1857)

Small cents:

• Flying Eagle (1856-1858)
• Indian Head (1859-1909)
• Lincoln Wheat (1909-1958)
• Lincoln Memorial (1959-2008)
• Lincoln Bicentennial 4 reverse designs (2009)
• Lincoln Union Shield (2010-)

Canada Reverse designs

1858-1920
The maple leaf wreath

1858-1911
This 1-cent coin features the design of L.C. Wyon of the Royal Mint. It portrays maple leaves wrapped around a vine.

1911-1920
W.H.J. Blackmore designed this reverse of the 1-cent coin. The representation of maple leaves wrapped around a vine was kept.

1920-1936
The two maple leaves
This design, created by Fred Lewis, coincided with a reduction in the 1-cent coin's diameter.

1937-1966, 1968-1981, 1997-present
The maple leaf twig (round coin)
In 1937, as part of an effort to modernize Canada's coins, G.E. Kruger-Gray created the maple leaf twig design. His initials appear on the right.

1967
The centennial 1-cent coin
Alex Colville created a special set of coin designs to commemorate the 100th anniversary of Canadian Confederation; the penny features a rock dove in flight.

1982-1996
The maple leaf twig (12-sided coin)
The shape of the maple leaf twig was altered to make identification easier for the visually impaired. The coin reverted to the round design in 1997.

Answer 2

Many major ones and a lot more minor ones. See the link for pictures